Micrometer height gauge



Patented Nov: 24, 1925.

ATE N T F l i GEORGE JHARDG-ROVE, 0F LOVELL, WYOMING.

' MICROIVETER HEIGHT GAUGE.

i 4Application filed June 8, 1923. Serial No. 644,203.

To all whom, t may concern.:

Be it known that I, GEORGE J. HAnneRovE, a citizengof the. United States, reslding at Lovell,\in the county of Big Horn and State height to one ten-thousandths of an inch/ Primarily the inventionhas for its object to provide agauge of the type stated w-hich ainging is capable of rapidly andaccurately truing up a piece of work in a lathe chuck and facing a surface parallel to one alreadyv facedi to within a ten-thousandth of an inchL and which is adaptable to use in connection with inilling machines, boringmachine, plan'ers and the like, in a manner Whereb .the vsame will effectively and practicall to eiiect'the desired gaugingfpr "hich it Ais designed, accurately and ina manner whereby the wasteful .cutand-try method commonlyemployedwill be eliminated.

The inventionmoreespecially yhas for its' objectto provide'agange of the typestated ink whichtlie parts-are designed for'eiectgraduated and cooperative in a. nner or effecting adjustments more minute and more easily readable than common intools of this' type, and in which provision isl made for so adjusting and operating the parts of the invention as to make provisionmot only for the normal range of actionof the same but also fora ject the provision of. means `whereby the United States standard, scale of measurement may be used in cooperationwith the other micrometer features of my v improved gauge.

With the above and otherl objects in view, the invention resides in those novel details l of construction, combination of andarra e.. ment of arts, all of `which Vwill be first filly described) pointed out in the appended claims, ,reference being had to the accompanying drawing, in which the figures are all shown on a somewhat enlarged scale for practical rea- SODS. s v

, ing gauge block in dotted lines.

:rear split bearing bushing..

- vfunction v.

.f' Figure 12 is a detail perspective view of a variation o increased ranges of action there- The invention still further has for its ob-i .after to be described.

in detail, then be specifically Figure 1 is a side elevation on an enlarged v scale of my invention, parts being' broken out `and in section, an extension memberJ being shown operatively app-lied to the slid- Figure 2 is a topj plan view ofthe base body.

Y Figure 3 is a detail view of the operating screw.v` v

Figure 4 is av detaii the turningjhead. Y

Figure 5 is a detailvperspective'view of the scale collar. l Figure' is detail perspective view of the bearing washer.

Figure 7 is a detail perspective view illustrating the pair of cooperating lock nuts. 7 Figure 8 is a detail perspective view of the Figure 9 is adetail perspective the front split bearing bushingf `Figure 10 is a detail .perspective view of 'thesliding-gauge.block. igure 11 is a detail side elevation of one 'f the extension members.

type of wrench which may be used in connection with the gauge.

Figure 13 vthat llustratedin Figure -1 and illustrates theA adaptation of the United States standard scale thereto.

In the .d1-swing, in whieh like ums-ais' of the figures, 1 90v indicate like parts in all inilicates .the base'bodyof my improved micrometer height gauge with whichr the sliding gauge block 2 slidably cooperates througlnthe action of the operating screw purposes herein 95 3. 1n a manner and for th Y The base -body Y1 hollowed as' at 4 to form a pair of opposlte side walls 5, a front. wall 6 and a rear wall 7.

rlhe front wall. 6 is provided with a socket 100 bore 8 for accommodating a split bearingl tin 14, which is adapte to be journale in 1.10

Y i j perspective view of ro l view'ioi 7 5 is a detail side elevation of a` i portion of the reverse side of mygauge to S5 the split bearing bushing 11 and a threaded outer end 15, the purpose of which will soon appear. Suitable set screws 16 are introduced into the front and rear walls 6 and 7 and are adapted to engage the split bearing bushings 9 and 11. By adjusting the set screws 16 the frictional contact of the bearing portions of the screw 3 within the saidV bushings may be adjusted to .edect such degree of rictional engagementY as may suit the desires of the us'er of my improved gauge.` It will also be readily understood that by these means .it is also possible to clamp the operating screw 3 to any partic- 'ular adjustment.

A scale collar l17 is threaded upon the outer Vthreaded end of the operating screw 3, and 'the rear wall 7 of the base body `1 is provifded with a counterbored socket 18 for accommodating the said scale collar.- A knurled turning head 19 is threaded upon the outer end of the threaded portion 15 of the operating screw 3 and the head acts as a 'turning medium for the said screw and alsoas a lock nut or` pro erly locking-the scale collar 17 in its re ation with the operating screw.

. The operating .screw 3 is securely held in rotative relation with the lase body and within the bearing bushings 9 and 1.1 b

reason of the relation ofthe scale collar 1 J with the rear wall 7 and?` in' the bearing socket 18 thereof, and a bearing washer 20 held i-n proper position in cooperative relation with theI bearing bushing 11, by apair of knurled lock nuts 21.`

The lock nuts 21, the scale collar 17 and the turning head 19 areeach provided with\ wrench holes 22 for accommodating the turning pin 23 of a wrench such as is indicated in Figure 12', and which may beelectively used in properly applying and adjusting the .mem ers hereinbefore referred to.

The vsliding 'gauge block v2`is provided with a height gauging face 24,' in which is provided a threaded aperture 25, is provided on its side faces with indicating mark ings. 500, as is indicated at 26,` anda A l marking, as is indicated at 27, on. the one oppositeside 4 It will i the foot and the outer face of the inclined portion of each vofthese side walls-5 is provided with scale markings, as is indicated' at 29, one'sider thereof, see .Figure 1 being marked in .a special manner, herelnafter referredtq iidthe opposite s1de,theeof being marked with the United ard scale.

In Figure 1 m improved micrometer height gauge is siown at the lowermost limit of its range of operation that is, the

States standheight gauge face 24 is there illustrated at the 3A height with the .500 marking indicated at 26, indicating the l height reckoned from the base of the base`body. This is the lowermost limit of the range of my improved gauge and, as will hereinafter be j readily apparent, the said gauge is capable of. properly gauging any desired height from this of an inch. Y

When using the parts shown in full lines in Figure :1 and with the instrument. de-

point upward in 'ten-thousandths signed with a limit of longitudinal travel of the block 2 of 2% inches the corresponding Vertical travel or height gauge range will be 1. For suitably taking care of greater ranges of height gauging than is possible in the structure shown 1n full lines 1n the iigure indicated, I have provided means for extending the range of the gauge, as will presently appear.

The sliding Agauge block 2 is provided with a pendent portion and a guide portion 31 which extend into the hollow portion 4 bf the base body 1 to move in close fit therewith under action of the operating screw 3 which cooperates with the threaded aperture 32 through'thependent portion30 fin effecting the longitudinal slidingof the said gauge block.

For properly providing for an extension of the range of actionof my gauge, as above indicated, I provideA one or more extension A lines i-n Figure 1, and these extension membersinclude a knurled portion 3'4, for facilitating thegquick application thereof in cooperation with the slidinggauge block 2, with the threaded shank 35` thereof threaded linto the socket 25 provided therefor in'the sliding gauge block. The extension member 33, illustrated in Figure 1, is a standard one finch extension, by the use ofiwhich the range of action of the gauge isincrased exactly one inchi The extension member may be members 33, such as is indicated indotted,

rovided with an intermediate 41 indicatn mg marking 36 for aidingintheA gauging g action. .u While I have illustrated` 1n Figurel a Aone inch 'extension member, i-tvwill be readi- Il -1 understood that extension members of like construction .but ,of varied standard sizes may -be used in connection with myA gaugeso that the range of action of -the ASallie may be extended to any'r degree without varying the accurate gauging of *heights inten-thousandths. For example, a 2 extension 37 is'indicatedin Figure 11, which extension is ofl like design as the extension illustrated in Figure 1, except `or itslengt-h.

Liscate@l lt will be also understood by reference to Figure 11 that each of these extension members may be provided at its upper gauging face with a threaded socket38 of such size as will readily accomodate the threaded shank 35 of another such extension meinber-so that two or several extension members may be used cooperatively foracquiring the desired gauging range. l

It will be readily understood that by turning the head 19 the sliding gduge block 2 vvill be moved longitudinally along the inclined portions 28' of the Walls 5 to thereby properly gauge the height in the accurate manner provided for by the special scale marking employed in my invention. v

In the practical development of my invention, the pitch of the threads of the main threaded portion 12'of the operating screw is forty threadsto the inch, so that by one complete revolution of the turning head 19, the sliding gauge block 2 will be moved longitudinally one-,fortieth of an inch. Each such movement of one-fortieth of an inch,

by reason of the exact incline of the Walls l 5 at 28 on an angle of 23 36.14 (4.8 rise per foot) effects a vertical movement of the sliding gauge block 2 of one one-hundredth of an inch.

By reference to Figures 1 and 5, itwill be observed that the scale collar 17 has the foi-e face thereof, which is in cooperative y sliding of an inch will be effected.

'principal divisibns, around the periphery thereof, which cooperate With a marking on the top face of the rear Wall 7 of the base body and which ure 2. ,i As before stated, one complete revolution of the turning head 19 effects a longitudinal movement of the slide block 2 ofone-fortieth of an inch and a vertical movement thereof of one onehundredth of an inch. From this, it will be readily apparent that a movement of the turning head a distance of one of the principal divisions indicated on the scale body 17, that is, one-tenth of a revolution, aV vertical movement of the gauge block 2 of one one-thousandth By reference tothe said Figures l and i it Will be observed that themain division of the scale collar 17 into tenths is again sub-divided, as is roughly indicated in those figures. In the practical development of my invention this sub-division-is in tenths so that the scale collar 17 is divided into sliding gauge block 2 of one-thousandth of. an inch: It will be just as readily'under stood that movement of the turning head 19 is indicated at 39 in Fig,

a distance of Ionevof the hundredths divisions of the scale collarwill effect a raising of the sliding gauge block 2 of one ten-thousandths of an inch.

Assume that the sliding gauge block- 2 'has a limit of movement of two and a half inches longitudinally, by reason of the degree of incline 28, a'norresponding vertical movement of one inch is effected. This coniplete longitudinal movement of two and ad half inches is effected by one hundred revolutions of the turning head 19, which will be apparent from the description foregoing.

The Aspecial sca-lemarkingl indicated at 29 in Figure l-shovvs a scale divided prilncipally into Vtenths and subldivided in onehundredths, the first one' of the one-hundredths divisions,that is the start of the scale, is marked .7 and is adapted to register With the 0 mark 27 on the sliding gauge block 2 and indicates a gauging height of the face 24 ofthe block 2 with relation to -the base of the base'body 1 of .750 or 5% of an inch, its lowermost adjustment.

Byreason of the cooperation of the sliding gauge 2 with the accurately designedinoline 28, and the cooperation ofthe accurately designed pitch of the operating screw 3, it is'possible to provide lmy micrometer gauge With scales which are mu h veasier to observe and read, considering t e great degree of/accura'cy of my invention, than is l possible in any conventional'type of micrometer gauge. .By .this special arrangement and cooperation of parts asabove del scribed it is possible for me to provide the graduations on my* improved gauge two and Va half times as far apart as is common on any standard scale. This feature proves very valuable to one 'using myimproved micrometer gauge Whose eye-sight has become impaired and Who Would indgreat diHiloo culty reading minute measurements by use of the almost infinitesimal giadationswhich would be necessary on a common typeofv micrometer gauge designed to function With the same degree of accuracy possible in the structure disclosed herein.

As before described, the gi'aduations il 1 lustrated in Figure 1 are of a special nature peculiar to the specific' functioning ofmy improved construction of micrometer gauge, that is they are divided into tenths andronehundredths to specifically cooperate with the graduations upon the collar scale 17.

'By reference to. Figure-13, it will be observed that the Aopposite side ofmy gauge to that illustrated inFigure '1' is provided With United States standard scale of gradu-l ation that is, in to inches and fractions of" an inch. The marking `.50() indicated at 2G on Figure 1 will, on this side,'be marked according to the United States standard scale one-half inch". The 0 marking indicated at l27 on Fi ure 1 will of course remainfthef l g 7.

l0 and a half times theirfnorma size, to greatthe scale collar 17, as hereinbefore described..

same but the .750 indicating the beginning of the scale in Figure 1 will, on this` side, be marked to the .United States standard scale three-quarters.

By reference to the figures indicated it will be readily understood that in utilizing the standard scale in cooperation with this ^micrometer, it is possible, for reasons above described, to make these gradations also two ly facilitate the ready observation and reading of -the height indicated. As above stated,

the range of longitudinal movement of the sliding gauge block 2 on the, inclines 28 and y 15 walls 5 1s two and a hal inches-'and in util- `fecting vizing the^ standard scale, as above referred. to, this path of travel of two and a half inches is made to represent a single United States standard inch of raduation, that is, the actual two and a halg inches may be divided according tothe United States standard scale measurement as though lit -ter height gauge.

of. an inch. .This willbe accomplished by further rotating the 'head 19 a distance equivalent to one of the major divisions of Thus it will be seen that the United States standard scale arrangement readily cooper-` ate's withv the special scale arrangement, the

screw, and the scale A,collar in efoperatingl A e very minute adlustments possi- 4ble by reason lof the peculiar construction and arrangement of my improved microme- B reason 4of the combination of scale mar ings, the angular base body, the sliding' gauge blockl and the operating screw divisions, it will be readily ap arent that were a single inch and be divided into by the 'use thereof one can rea ily and ac'- halves, quarters, thirty-seconds and sixtyfourths, as is common in such sales.

By thus providing the opposing side of my gauge body 'with the standard scale and forming the individual markings thereof two and a half times their-usual size, it will curately true up a piece of work 1n a lathe chuck and face a parallel surface to one already faced to within a ten-thousandth of an inch, by placing the base of the gauge against the chuck face and using the sald sliding gauge block for truing the vwork be readily apparent that the movement of through the action of the operating screw the turning head 19 will, in the manner 3, as before described. above described, effect longitudinal movethe. United States standard scale, that is, gauge at the required of vertical movement. It will be readily unment of the gauge block 2, the degree of' such movement being clearly indicated on should the turning head 19 be given` one hundred complete revolutions the mark'27 on the gauge block 2 will register one inch Vderstood that the lesser degrees of vertical movement thus effected through rotation of the turning head 19 will be accurately indicated on the standard scale.

, By thus providing the standard scale 'and arranging the same as above described, it

will'also be readily a parent that the said actly it will be rea understood that r in order to adjust .thegauge to `the height desired, movement vertically of the slidin gau'geblock to the extent of a quarter o an inch plus one-thousandth-will have to be effected. Inasmuchas the 0 mark on the gauge block is, when the parts are positioned as shown inv Figure .1, in register with with gbut slight vmodification it f ma It will also be readily apparent to anyone familiar with4 milling machines, boring mills, planers and sha ers, by setting the iieightV and Vbringing the cutting tool in contact with the same, that the cut can be taken accurately, therebyeliminating entirely a cut and try method and all of ther waste of material and time incident thereto.

By reason of the combination and cooperation of the scale arrangements, special and United Statesstandard, quick and'accurate readings may be made and by reason of the actual markings .being two and a half times the usal size, made possible by the incline arrangement, reading may be made by persons wlth slightly impaired eye-sight which could not be possible with -the conventional types' of scales. TheaOQ'parallel line 26. on one side of the Slide block and the 1/2 inch line on the other side of.. the block, also the circular graduation 3 6 on the extension rods are placed there for the rpurpose of setting a surface gauge. While I have illustrated my invention as especially desi i for use. withthe stands ard scale (Eng ish system)` it is obvious thla adapted A:for use with scales graduate according to the metric system.

The e'nd of the screw 13 where it engages 1- the zal, the starting mark 'on the United the-walls e (ses. Figure 1) is pri-,family States standard scale, it' is a thel head 19vwould be revolve until the 0 parent that convex ,to'reduce the area of contact and thus reduce friction at thatplaoe.

lll

From the foregoing description, taken 'in connection with the accompanying drawing, it is thought the complete construction, operation and advantages of my invention will be readily understood by those skilled in the artto which it appertains.

What I claim is: -1. A device of fthe class described, comprising a body having a base and an inclined surface, theinclination f which to the base is at an angle of 2 36.14', saidl body having a pair of screw bearings, the axes of which lie at the saine inclination as that of the inclined surface of 4the body, a screw rotatably held in said bearings against longitudinal movement and having a pitch of forty threads per inch, a movable member mounted to slide on the inclined surface of said body and having a threaded portion to engage said screw, saidbody having a scale associated with said inclined surface and said movable member, and means by which said screw may be turned.

2. A device 'of the class described, comprising a body having a base and an inclined surface, the inclination of which to the base is at an angle of 23 36.14 the said body having a pair df screw bearings, the axes of which lie at the same inclination as that of theincline'd surface of the body, a screw rotatably held in said bearings against Ylongitudinal movement and having a pitch vof forty threads per inch, a movable mem-r ber mounted to slide `on the inclined surface surface of said body andhaving a portion mounted in said upper and lower bearing?,A

projectinginto the recess therein, an' adjusting screw engaging said portion arid being and means by which said screw --may turned to adjust the position of said slide.

4. In a deviceof the class described, a body living a'base and, an inclined surface,said body being recessed in said inclined surface and provided with upper and lower screw bearings, a slide mounted on said inclined surface of said body and havinga portion projecting into the recess therein, an adjustv ing screwy engaging said portion'and being mounted in said Vupper and `lower bearings, means by which said screw may be turned to adjust the position of sai-d slide, and means to hold said screw against. longitudinal movement in its bearings, saidmeans comprising jamb nuts and washer' with provi-- sion for taking up wear.

5. In a device ofthe class described, a body having a base andan inclined surface, said body being recessed in said inclined surface l and "provided with upper and lower screw bearings, a slide mounted onsaid inclined surface of said body and having a portion projecting into the recess therein, and adjusting screw engaging said portion and being mounted in said upper and lower bearings,' means by 'which said screw may be turned to adjust the position of said slide, i

split bushings in said screw bearings, and

means engaging said bushings to adjust j their gripping action on the screw. v

6. In a device f the class described, a body having a base and an inclined surface and graduations constituting a scaleadjacent to said inclined surface, said body also having a screw bearing with split bushing and bush ing adjusting screw, 'a movable .member mounted on said body to move along its inclined surface, an adjustin screw mounted in said screw bearing an engaging said movable member and having a smooth bearing surface with threaded surfacesl at each` side of said bearing surface, a scaled collar `and a turning head threadedon one end of said adjusting screw, said body being en gagedrby said collar, a washer and jambnut on sai collar to hold the screw against longitudinal ymovement in its bearing, substantially as shown and described. j

7, A device of the 'class described comprisng a, body, a member cooperative withsaid body and movable -longitudinally and vertically with relationto the bottom of said screw to cooperate with said scale body, means whereby the said member may be mov-ed in such manner that the longi-z tudinal movement thereof will be greater than tle verticaL movement thereof, and

said body having a plurality of measuring scales cooperatively arranged for indicating standard and decimal fractions of inch movement `of said movable member said means whereby said member may be moved comprising an adjusting screw, said body haviiig fbearings rin whichn said -screw l1s mounted and means in said bearings for taking .up wear. 8. A device' ofr theA class described comprisiiig a' body, a member cooperative with said body and movable longitudinally and vertically. with relationto the bottom of saidbody, means"'wheieby the said member may be moved in such manner that the longitudinal movement-thereof will be greater than the vertical movement thereof, and a `lural ity of measuring scales cooperative y arranged for indicating standard and decimal fractionsof inch movement of said -movable member, said means whereby said'member through one o said bearings, said bo y havmay be moved comprising an adjusting screw, said body having bearings in which said screwis mounted, means in saidl bearings for takin up wear, said screwI assing ing a recess, a member on said screw entering said recess, and jamb nuts and washer on said nscrew adjacent to one of the bearings for holding the screw against longitudinal 10 movement.

9. 'A deviceof the class described compris- .l ing a body, a member cooperative with said body and movable longitudinally and verticallywith relation to the bottom of said 1,5 body, means whereby the said member may be moved in such manner that the longitudinal Lmovement thereof will be reater than .the vertical movement `thereoiy, said body having' measuring and indicating l scales, arranged whereby movement ofthe 'movable member may be measured and whereby'longitudinal movement of the said movable member .will eliect an indication.

of the degree of 'vertical movement thereof,

2i and adjustable means whereby the range of use of -said device may be varied at will, said means lwhereby said member may be l moved including asfeed screw, said body having a thrust bearing in which one end 30 of said feed screw lies, s aid body having another bearing through which said feed screw projects, and janib nuts and washer on sai screw engaging said other bearing to ,maintain said screw in the 'thrust bear- 'ing against longitudinal movement and v-to take up wear. c

- 10. A-device'of the class described comprising a bodywhich includes an inclined portion, a movable member slidably cooperav tive with said inclined portion, means for moving said mov-able member along said inclined portion, and said body having measuring and indicating scales for measuring and'indicating the movement 'of s aid `mov- Y able member, said moving means including a feed screw', said body having bearings for said feed screw, oneof which constitutes a thrustbearing, means for holding the screw in its bearings against longitudinal Amovement away from the thrust bearing, and connections between said movable membei' and said screw.

' 11. A device of the biass'aescfibea am. -`'prising a body which ,includes an inclined v rtion, a movable .member slidably cooperative with said inclined portion, .means for moving said movable member along said inable member, said moving means Vinclud,-

ing an indicating scales for' measuring and indicating the movement of said mov- Ving' a feed screw, saidbody having bearfor said feed screw, one of which constitutes a thrust bearing,means*for hold- `ing the screw in its bearings again`st1ongi`r clined s ortion, said body having measur- Lacanaul tudinal movement away from the thrust bearing, connections ,between said movable member and said screw, and means in said bearings whereby the turning movement of said screw may be tightened or loosened as/ desired.

12. A' device of the class described comprising a base bodyghaving a flat base and an inclined\portion a slidable gauge block co.

Y operative with said body and slidable along the inclined portion thereof, a yscrew mounted on said lbody for moving said gauge block, means for `measuring rotation .of said screw, a turning head on said screw for rotating the-V same, and cooperative measuring and indicating scales arranged f prising a base body, having a flat base and a i portion inclined atx the rate of 4,8 per foot,

a slidable gauge block cooperative with said bodyl and slidable along the inclined portion thereof, a screw mounted/on s id body,.cooperative with said gauge bloc for sliding the' same and 'having a pitch of forty threads to the inch, a turning head on said' screw for rotating the same, means for measiiring rotationof said screw, and cooperative measuring and indicating scales arranged whereby movement of the slidable gauge block may be measured and whereby longitudinal movement of said slidable gauge block alongsaid inclined portion will eil'ect a registeringV of the degree of vertica-l movement thereof up said incline.

j 14. A device` of the class described com- Y prising a base body having a flat ba e and aninclined portion and being hollowe to provide side walls and front and rear end walls, a slidablegauge block cooperative with said body and slidable along .the inclined portion thereof, said gauge blockhaving-a height measuring marking thereon, a 4ortion pendent from said gauge block a apted to -b`e guided'in the hollow'of said base -body and having of threaded aperture, a screw4 for moving said gauge blocks lit bearingsforsaid screw in'tlierfront an rear walls of said frictional engagement of said bearings with said screw, a turning head on said screw for rotating the same, said screw having means for measuring its rotation, said base 4body base body in which thesaid screw may rotate on an axis parallel to' the inclined portion-of the' base bod means-for adjusting'.

having a measuringscaleat onexside :for-cov operating with the marking on that side of the gauge block, the'individiial divisions of 'tieally' a path atan vsenile two and a half times as lonhhg as the actual verticalY lift which they cette.'

bearing bushings mounted humid'- bearings of the base, means carried by the base and -20 engaging said bushngsf for .their A 15.` fmicrometei' Vheight comprisgriimg tension, a. feed screw mounted in 6 ing a base, a nge block,"ln'eans to move Said sai ushings, a. gauge block slidably mountblock along e base longitudinally and vered on said inclined surfece and having a, 1"-

angle 23 36,14! tim pro ectecl into thebnse and engag by f abase hevingra; su

15 hase andA slotted through said inclined sur- (4.8 rise per foot) to the base horizontal,

; a decimal scale on the Vbase to indicate the 10 heights to which the block 'bs/movedLand a smaller division scale cooperating with the blockmo 'means and the decimal scale.

16. A micrometer he'ht gang; compriswe' inc base having aiair of screw 'receivmg bea. the axes o which coincide and'- lie pnrall with iaid surface, split ed'to the.v

said fee screw, one end of'said eed'srewbein convexed to'engage'a, wall in; one of the rings of said base, thereby actingas a thrust bearing, and means on said screw and engaging the bese formainta' contact between said screw end and the ud]acent surface of the base bearing in, which itis mounted, 4and meansby which said screw muv be turned to adjust the position-1 of saidgage block-along seid inclined Y GEORGE J: HAR 1)Gr1zov1sY.VV f 

